Homology, Homotopy and Applications

Volume 20 (2018)

Number 2

A Seifert–van Kampen theorem in non-abelian algebra

Pages: 79 – 103

DOI: http://dx.doi.org/10.4310/HHA.2018.v20.n2.a5

Authors

Mathieu Duckerts-Antoine (Departamento de Matemática, Universidade de Coimbra, Portugal)

Tim Van Der Linden (Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

We prove a variation on the Seifert–van Kampen theorem in a setting of non-abelian categorical algebra, providing sufficient conditions on a functor $F$, from an algebraically coherent semi-abelian category with enough projectives to an almost abelian (= Raikov semiabelian) category, for the preservation of pushouts of split monomorphisms by the left derived functor of $F$.

Keywords

derived functor, fundamental group, homology coproduct theorem, categorical Galois theory, algebraically coherent semi-abelian category

2010 Mathematics Subject Classification

18A40, 18G10, 18G50, 20J99, 55N99

Full Text (PDF format)

Received 24 January 2017

Published 2 May 2018